alleryIf $n(A)=3$ and $n(B)=2$, then $n(A\times B)$ equals:
- 6
- 5
- 9
- 8
Show answer and solution
Correct answer: A. 6
We have n(A×B) = n(A)·n(B).
That is n(A×B) = 3·2.
So n(A×B) = 6.
GRE Sets and Relations — practice questions — page 2
Explore 101 free Sets and Relations questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 31–60 of 101.
If $n(A)=3$ and $n(B)=2$, then $n(A\times B)$ equals:Read the answer and worked solution →The Cartesian product $A\times B$ is the set of all:Read the answer and worked solution →If $n(A)=2$ and $n(B)=3$, the number of relations from $A$ to $B$ is:Read the answer and worked solution →If $n(A)=2$ and $n(B)=3$, the number of functions from $A$ to $B$ is:Read the answer and worked solution →The domain of the function $f(x)=\dfrac{1}{x-2}$ is:Read the answer and worked solution →The range of the function $f(x)=x^2,\; x\in\mathbb{R}$ is:Read the answer and worked solution →The domain of $f(x)=\sqrt{x-1}$ is:Read the answer and worked solution →If $(x+1,\,y-2)=(3,\,1)$, then $(x,y)$ equals:Read the answer and worked solution →The domain of $f(x)=\sqrt{4-x^2}$ is:Read the answer and worked solution →If $f(x)=x^2+1$, then $f(2)$ equals:Read the answer and worked solution →A relation $f$ from $A$ to $B$ is a function if every element of $A$ has:Read the answer and worked solution →In mathematics, a SET is defined as:Read the answer and worked solution →Which symbol denotes 'belongs to' / 'is an element of' in set theory?Read the answer and worked solution →The set of all letters in the word 'SCHOOL' in roster form is:Read the answer and worked solution →The set A = {x : x is a positive integer and x² < 40} in roster form is:Read the answer and worked solution →Which of the following is an EMPTY set?Read the answer and worked solution →Let A = {x : x is a natural number which divides 42}. Set-builder form A in roster form is:Read the answer and worked solution →Set A = {x : x = n/(n+1), where n is a natural number and 1 ≤ n ≤ 6} in roster form is:Read the answer and worked solution →Which set is FINITE?Read the answer and worked solution →For the equation x² + x − 2 = 0, the solution set in roster form is:Read the answer and worked solution →Set X = letters in 'ALLOY'; set B = letters in 'LOYAL'. Compare:Read the answer and worked solution →Let A = {n ∈ ℤ : n² ≤ 4} and B = {x ∈ ℝ : x² − 3x + 2 = 0}. Are A and B equal?Read the answer and worked solution →Which statement about the EMPTY SET ∅ is INCORRECT?Read the answer and worked solution →Which collection is NOT a well-defined set?Read the answer and worked solution →A = {1, 3, 5} and B = {x : x is an odd natural number less than 6}. What is the relationship?Read the answer and worked solution →For A = {1, 2, 3}, identify which is a PROPER subset of A.Read the answer and worked solution →The graph of $f(x) = 1/x$ in $\mathbb{R} - \{0\}$ is:Read the answer and worked solution →Which of the following is a linear equation in one variable?Read the answer and worked solution →Solve for t: 5t − 3 = 3t − 5Read the answer and worked solution →Solve for y: 2y + 5/3 = 26/3 − yRead the answer and worked solution →
Worked practice questions
The Cartesian product $A\times B$ is the set of all:
- subsets of A and B
- ordered pairs $(a,b)$ with $a\in A,\,b\in B$
- unordered pairs from A and B
- elements common to A and B
Show answer and solution
Correct answer: B. ordered pairs $(a,b)$ with $a\in A,\,b\in B$
A×B is the set of all ordered pairs (a,b) with a∈A and b∈B.
If $n(A)=2$ and $n(B)=3$, the number of relations from $A$ to $B$ is:
- 9
- 6
- 64
- 8
Show answer and solution
Correct answer: C. 64
A relation from A to B is any subset of A×B; number = 2^{n(A)·n(B)} = 2⁶ = 64.
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